Like the laws of today, Hammurabi's Code lays out specific punishments for specific crimes. This is meant to create equity in the way that punishments are meted out. Both the Babylonians and today's society have a strong desire for the application of justice. That is ultimately why legal systems are...
created. In a just society, people need to be held accountable for their actions which harm others. A legal system helps to ensure this.
However, unlike today, Babylonian punishments vary depending on one's social class. While in practice, certain populations today are disproportionally punished for some crimes, this is not enshrined in official law. The modern legal code does not differentiate between social class.
Like today's legal system, Hammurabi's Code lays out the way that trials are conducted. It spells out the requirement for witnesses and impartial judges. Unlike today, though, an accuser in Babylonian times was responsible for bringing the accused to court rather than law enforcement.
A major difference between Hammurabi's Code and today's legal system has to do with the form of punishments. It is true that some punishments are very similar. Today, some civil and criminal infractions result in the payment of damages and restitution. There are examples of this all over Hammurabi's Code. However, most crimes today result in incarceration. The Babylonians did not use incarceration as a common punishment.